The reason the shadows on object look different then the shadows on the environment background is that they are not created in the same way. The shadows on the objects are created from the sun and environment and are accurate. The shadows projected on the environment floor plane are created by an omni light and therefore not as accurate. It is always a better idea to have your own floor rather then using the environment floor plane if you are looking for accurate shadows. If you want to use the Showcase environment floor, here are few things you might want to try:
1-Go to the Appearance menue>Directional light and Shadow. Under the Shadow Properties for All environments, uncheck the Softness option. This will give you sharp and more accurate shadows on your ground plane. This will also help increase the frame rate display in Showcase which is a plus. You might have to increase the Resolution of the shadows to 4096 x 4096 to avoid pixelated shadows.
2- Adjust the Shadow intensity and try to find a happy medium between both type of shadow.
3-if you are using your own ground, go to the Shadow Casting for All environment tab and change the option to be: Shadows are cast by: all objects on: Objects. This will stop the Showcase ground plane to receive shadows from the objects.
Hope this helps.
Marion